Question

A rectangular parallelepiped with edges along x, y, z axis has length 3, 4, 5 respectively. Fiind the shortest distance of the body diagonal from one of the edges parallel to z-axis which is skew to the diagonal

• A. $\frac{16}{5}$
• B. $\frac{15}{\sqrt{34}}$
• C. $\frac{12}{5}$
• D. $\frac{9}{5}$

Answer 1

Answer: (C)

$\frac{12}{5}$

Answer 2

The equation of diagonal OE $\vec{r}$ = 0+λ(3$\hat{i}$+4$\hat{j}$+5$\hat{k}$)

equation of edge GD
$\vec{r}$ = 4$\hat{j}$ + $\mu\hat{k}$
shortest distance = |projection of 4$\hat{i}$ on (3$\hat{j}$ - 4$\hat{i}$)|
= $\frac{12}{\sqrt{9+16}}$ = $\frac{12}{5}$

So, the correct answer is (C): $\frac {12}{5}$